Dynamic strength of molecularly bonded surfaces

Size, Kinetics, and Free Energy of Clusters Formed by Ultraweak Carbohydrate-Carbohydrate Bonds

Weak noncovalent intermolecular interactions play a pivotal role in many biological processes such as cell adhesion or immunology, where the overall binding strength is controlled through bond association and dissociation dynamics as well as the cooperative action of many parallel bonds. Among the various molecules participating in weak bonds, carbohydrate-carbohydrate interactions are probably the most ancient ones allowing individual cells to reversibly enter the multicellular state and to tell apart self and nonself cells. Here, we scrutinized the kinetics and thermodynamics of small homomeric Lewis X-Lewis X ensembles formed in the contact zone of a membrane-coated colloidal probe and a solid supported membrane ensuring minimal nonspecific background interactions. We used an atomic force microscope to measure force distance curves at Piconewton resolution, which allowed us to measure the force due to unbinding of the colloidal probe and the planar membrane as a function of contact time. Applying a contact model, we could estimate the free binding energy of the formed adhesion cluster as a function of dwell time and thereby determine the precise size of the contact zone, the number of participating bonds, and the intrinsic rates of association and dissociation in the presence of calcium ions. The unbinding energy per bond was found to be on the order of 1 kBT. Approximately 30 bonds were opened simultaneously at an off-rate of koff = 7 ± 0.2 s(-1).

BROWNIAN DYNAMICS SIMULATION OF CATCH TO SLIP TRANSITION OVER A MODEL ENERGY LANDSCAPE

We perform Brownian dynamics simulation (BDS) of catch to slip transition over a model energy landscape. Through our BDS we demonstrate that for forces below the critical force the bond rupture occurs mostly through the catch pathway while for forces above the critical force the bond rupture occurs mostly through the slip pathway. We also demonstrate that the shoulder in the bond rupture force distribution switches to peak as the loading rate increases progressively and the bond lifetime is maximized at the model dependent critical force. The force dependent bond lifetime obtained via transforming the bond rupture force distribution at a given loading rate is in excellent agreement with that obtained from our BDS at constant forces. An alternative to the current mechanism of catch to slip transition is presented and validated through BDS.

Analytic descriptions of stochastic bistable systems under force ramp

Solving the two-state master equation with time-dependent rates, the ubiquitous driven bistable system, is a long-standing problem that does not permit a complete solution for all driving rates. Here we show an accurate approximation to this problem by considering the system in the control parameter regime. The results are immediately applicable to a diverse range of bistable systems including single-molecule mechanics.

Stochastic simulation of single-molecule pulling experiments

Single-molecule pulling experiments are widely used for studying the structure, dynamics, and function of single biological molecules via applying mechanical forces on them in a controlled way. Pulling at a constant speed or at a constant force builds up a mechanical force on a molecule or molecular complex leading to a molecular transition such as the dissociation of a molecular complex, unfolding of a protein, or unwrapping of a higher-order structure. We perform Brownian dynamics and Monte Carlo simulations of single-molecule pulling experiments. Through our simulations we demonstrate that the molecular transition rate based on the Kramers theory in the high-barrier limit becomes unsuitable as the applied force approaches the critical force at which the barrier disappears. We also demonstrate that use of molecular transition rate based on mean first passage time (MFPT) approach would be more relevant in describing molecular transition especially as the applied force approaches the critical force.

Force spectroscopy of polymer desorption: theory and molecular dynamics simulations

Forced detachment of a single polymer chain, strongly adsorbed on a solid substrate, is investigated by two complementary methods: a coarse-grained analytical dynamical model, based on the Onsager stochastic equation, and Molecular Dynamics (MD) simulations with a Langevin thermostat. The suggested approach makes it possible to go beyond the limitations of the conventional Bell-Evans model. We observe a series of characteristic force spikes when the pulling force is measured against the cantilever displacement during detachment at constant velocity vc (displacement control mode) and find that the average magnitude of this force increases as vc increases. The probability distributions of the pulling force and the end-monomer distance from the surface at the moment of the final detachment are investigated for different adsorption energies ε and pulling velocities vc. Our extensive MD simulations validate and support the main theoretical findings. Moreover, the simulations reveal a novel behavior: for a strong-friction and massive cantilever the force spike pattern is smeared out at large vc. As a challenging task for experimental bio-polymer sequencing in future we suggest the fabrication of a stiff, super-light, nanometer-sized AFM probe.

Statistics of reversible bond dynamics observed in force-clamp spectroscopy

We present a detailed analysis of two-state trajectories obtained from force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the unique possibility to vary the equilibrium constant in two-state kinetics, for instance, the unfolding and refolding of biomolecules, over many orders of magnitude due to the force dependence of the respective rates. We discuss two different kinds of counting statistics, the event counting usually employed in the statistical analysis of two-state kinetics and additionally the so-called cycle counting. While in the former case all transitions are counted, cycle counting means that we focus on one type of transitions. This might be advantageous in particular if the equilibrium constant is much larger or much smaller than unity because in these situations the temporal resolution of the experimental setup might not allow to capture all transitions of an event-counting analysis. We discuss how an analysis of FCS data for complex systems exhibiting dynamic disorder might be performed yielding information about the detailed force dependence of the transition rates and about the time scale of the dynamic disorder. In addition, the question as to which extent the kinetic scheme can be viewed as a Markovian two-state model is discussed.

Design rules for biomolecular adhesion: lessons from force measurements

Cell adhesion to matrix, other cells, or pathogens plays a pivotal role in many processes in biomolecular engineering. Early macroscopic methods of quantifying adhesion led to the development of quantitative models of cell adhesion and migration. The more recent use of sensitive probes to quantify the forces that alter or manipulate adhesion proteins has revealed much greater functional diversity than was apparent from population average measurements of cell adhesion. This review highlights theoretical and experimental methods that identified force-dependent molecular properties that are central to the biological activity of adhesion proteins. Experimental and theoretical methods emphasized in this review include the surface force apparatus, atomic force microscopy, and vesicle-based probes. Specific examples given illustrate how these tools have revealed unique properties of adhesion proteins and their structural origins.

Dynamic force spectroscopy: Analysis of reversible bond-breaking dynamics

The problem of diffusive bond dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e., under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach each other as the system reaches equilibrium. We investigate the dependence of the rupture force distributions and mean rupture forces on external parameters such as cantilever stiffness and influence of a soft linker. We find that depending on the implementation of a soft linker the equilibrium rupture force is either unaffected by the presence of the linker or changes in a predictable way with the linker compliance. Additionally, we show that it is possible to extract the equilibrium constant of the on and off rates from the determination of the equilibrium rupture forces.

Force-clamp spectroscopy of reversible bond breakage

We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the statistical properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple kinetic models. In the calculations, we explicitly exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Whereas for two-state behavior Poisson or sub-Poisson statistics of the events is found, we show that for more general kinetic schemes also super-Poisson statistics can occur. Temporal fluctuations of the transition rates, a hallmark for the presence of dynamic disorder, should become experimentally accessible via the determination of the second moment of the event-number distribution.

Is cell rheology governed by nonequilibrium-to-equilibrium transition of noncovalent bonds?

A living cell deforms or flows in response to mechanical stresses. A recent report shows that dynamic mechanics of living cells depends on the timescale of mechanical loading, in contrast to the prevailing view of some authors that cell rheology is timescale-free. Yet the molecular basis that governs this timescale-dependent behavior is elusive. Using molecular dynamics simulations of protein-protein noncovalent interactions, we show that multipower laws originate from a nonequilibrium-to-equilibrium transition: when the loading rate is faster than the transition rate, the power-law exponent alpha(1) is weak; when the loading rate is slower than the transition rate, the exponent alpha(2) is strong. The model predictions are confirmed in both embryonic stem cells and differentiated cells. Embryonic stem cells are less stiff, more fluidlike, and exhibit greater alpha(1) than their differentiated counterparts. By introducing a near-equilibrium frequency f(eq), we show that all data collapse into two power laws separated by f/f(eq), which is unity. These findings suggest that the timescale-dependent rheology in living cells originates from the nonequilibrium-to-equilibrium transition of the dynamic response of distinct, force-driven molecular processes.

Molecular energy dissipation in nanoscale networks of Dentin Matrix Protein 1 is strongly dependent on ion valence

The fracture resistance of biomineralized tissues such as bone, dentin, and abalone is greatly enhanced through the nanoscale interactions of stiff inorganic mineral components with soft organic adhesive components. A proper understanding of the interactions that occur within the organic component, and between the organic and inorganic components, is therefore critical for a complete understanding of the mechanics of these tissues. In this paper, we use Atomic Force Microscope (AFM) force spectroscopy and dynamic force spectroscopy to explore the effect of ionic interactions within a nanoscale system consisting of networks of Dentin Matrix Protein 1 (DMP1) (a component of both bone and dentin organic matrix), a mica surface, and an AFM tip. We find that DMP1 is capable of dissipating large amounts of energy through an ion-mediated mechanism, and that the effectiveness increases with increasing ion valence.

Stability of adhesion clusters and cell reorientation under lateral cyclic tension

This work is motivated by experimental observations that cells on stretched substrate exhibit different responses to static and dynamic loads. A model of focal adhesion that can consider the mechanics of stress fiber, adhesion bonds, and substrate was developed at the molecular level by treating the focal adhesion as an adhesion cluster. The stability of the cluster under dynamic load was studied by applying cyclic external strain on the substrate. We show that a threshold value of external strain amplitude exists beyond which the adhesion cluster disrupts quickly. In addition, our results show that the adhesion cluster is prone to losing stability under high-frequency loading, because the receptors and ligands cannot get enough contact time to form bonds due to the high-speed deformation of the substrate. At the same time, the viscoelastic stress fiber becomes rigid at high frequency, which leads to significant deformation of the bonds. Furthermore, we find that the stiffness and relaxation time of stress fibers play important roles in the stability of the adhesion cluster. The essence of this work is to connect the dynamics of the adhesion bonds (molecular level) with the cell's behavior during reorientation (cell level) through the mechanics of stress fiber. The predictions of the cluster model are consistent with experimental observations.

Actin binding of ezrin is activated by specific recognition of PIP2-functionalized lipid bilayers

In a quantitative manner, we investigated the mechanism of switching ezrin from the dormant to the active, F-actin binding state by recognition of PIP 2. For this purpose, we established a novel in vitro model mimicking ezrin-mediated membrane-cytoskeleton attachment and compared the F-actin binding capability of ezrin that either had been coupled via a His tag to a lipid bilayer displaying Ni-NTA or had been bound to supported membranes containing PIP 2. Epifluorescence and colloidal probe microscopy (CPM) were employed to demonstrate ezrin's conformational switch into an active conformation capable of binding F-actin. Epifluorescence images revealed attachment of fluorescently labeled F-actin solely to PIP 2-bound ezrin. For the first time, colloidal spheres equipped with an artificial cytoskeleton composed of firmly attached F-actin filaments were used to measure quantitatively the maximal adhesion forces and the work of adhesion of the ezrin-F-actin interface. We found that the work of adhesion between PIP 2-bound ezrin and F-actin is substantially larger than that measured between F-actin and ezrin bound to the membrane via the His tag. Collectively, these data indicate that activation of ezrin can occur as a consequence of PIP 2 binding and does not require additional cofactors.

Direct Measurement of Mechanical and Adhesive Properties of Living Cells Using Surface Forces Apparatus

The adhesive and mechanical properties of living cells assembled into a monolayer on two different substrates were investigated using the surface forces apparatus (SFA) technique. The force measurements allowed elastic and bending moduli of the cells plated on substrates to be determined. The moduli are in good agreement with data reported in the literature for single cells determined using atomic force microscopy. Results confirm that the nature of the cell–substrate interactions can mediate cell mechanical and adhesive properties.